Question: Multiply the following complex numbers, marked as blue dots on the graph: $(5 e^{\pi i / 4}) \cdot (1)$ (Your current answer will be plotted in orange.)
Explanation: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $5 e^{\pi i / 4}$ ) has angle $\frac{1}{4}\pi$ and radius $5$ The second number ( $1$ ) has angle $0$ and radius $1$ The radius of the result will be $5 \cdot 1$ , which is $5$ The angle of the result is $\frac{1}{4}\pi + 0 = \frac{1}{4}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{1}{4}\pi$.